Applications of lattice theory to graph decomposition (Q911609)

It is shown that the set of multitree classes equipped with a partial order is a lattice called a multitree lattice. This multitree lattice in fact is a geometric lattice. Since there is a one-to-one correspondence between a multitree class and an element of the multitree lattice, the trees of a composite of subgraphs can be generated without duplications by the set union of the Cartesian products of the multitree classes of the subgraphs, which form a maximal independent set.